WITHINGTON GIRLS SCHOOL

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1 Name Examination Number Room Number WITHINGTON GIRLS SCHOOL ENTRANCE EXAMINATION 206 MATHEMATICS PAPER 2 TIME: 40 MINUTES Some questions paper involve new ideas, but there are examples to guide you and help you understand these new ideas. Look at the examples carefully and try to answer all the questions. If you cannot answer a question, leave it and go on to the next one. Use any time you have left to check your answers and go back to any questions you have left out. CALCULATORS MUST NOT BE USED PAPER 2 TOTAL Marker s Initials Checker s Initials

2 Can you crack the code and translate the message? A ball of string contains 7 metres. It is cut into 20 cm lengths. 2 (a) How many pieces can be made? (b) How much string is left? cm 3. Here are two sequences of numbers The number 0 is in both sequences. What are the next two numbers that are in both sequences? 4. Place the numbers Answer grid in the grid so that the product (multiplication) of the numbers in each vertical and horizontal line equal to 36. Below are some grids to try out your ideas. Put your final answer on the big grid on the right. Page 2

3 5. Alice buys 6 packets of pasta. Each packet of pasta costs 95 pence. She also buys 5 packets of rice. In total she spends.70. How much does a packet of rice cost? 6. Jamie-Anne and Natasha both collect stamps. The ratio of the number of stamps is 5:3. If Jamie-Anne has 8 more stamps than Natasha, how many stamps do they have in total? stamps 7. (a) Ellie has 240 sweets. Each week she buys 45 new sweets and eats 60 old ones. After how many weeks will she have 50 sweets left? weeks (b) Sophie has 320 sweets. Each week she buys 30 new sweets and eats some old ones. After 7 weeks she has 348 sweets. How many sweets does she eat each week? sweets 8. What is the size of angle a? Diagram not to scale o PLEASE TURN OVER Page 3

4 9. Look at the number line AB. A B C and D are points on the line AB. (a) AC= 3 AB. What number is C? (b) AD= 3DB. What number is D? 0. There are 20 questions in a quiz. Points are awarded in the following way 4 points for a correct answer 0 points for questions unanswered 3 points for questions answered incorrectly (a) Leah answers 0 questions correctly, 3 incorrectly and left 7 blank. What was her total score? (b) Tammy s total score was 37 and answered 3 questions correctly. How many questions did she answer incorrectly? (c) Nicole got a score of 5 and answered 7 questions incorrectly. How many questions did she answer correctly? Page 4

5 . A quick way to subtract two square numbers is to use the rule a 2 b 2 = (a + b)(a b) For example = (26 + 6)(26 6) = 42 0 = 420 Use this rule to work out (No marks will be award if you do not use the rule.) 2. In the Debenham s sale everything is reduced by 25%. (a) What is the sale price of a Segway which originally cost 300? OFF 25% (b) The sale price of a jumper was 24. How much did it cost originally? NOW These are powers of x For example (a) What is ? x 2 = x x x 3 = x x x x 4 = x x x x 2 3 = = 8 (b) x 4 = 8, what is x? (c) What numbers are and if 2 3 = 72 = = PLEASE TURN OVER Page 5

6 4. Fill in the missing gaps (a) 25% of 32 = % of 40 (b) 40% of 35 = 50% of (c) 3 8 of 6 = 2 9 of 5. The diagram shows 3 identical triangles A, B and C. 80% of triangle A is shaded. 60% of triangle C is shaded. What percentage of triangle B is shaded? % 6. In 7W there are 28 girls. 20 like One Direction. 7 like The Vamps. 5 like both One Direction and The Vamps. How many girls like neither One Direction nor The Vamps? 7. Ana is 6 cm taller than Olaf. Kristoff is five and a half time the height of Olaf. Ana is 50 cm. How much taller is Kristoff than Ana? cm Page 6

7 8. An estimate for the area of a circle, radius r, is For example Area = 3 r 2 = 3 r r Area = = = 3 6 = 48 cm 2 4 cm (a) Find an estimate for the area of the circle. 6 cm cm 2 (b) Find an estimate for the area of this shape. 8 cm 8 cm cm 2 (c) An estimate for the area of the circle is 47 cm 2. Find the radius of the circle. r cm cm 2 (d) The area of this shape is 25 cm 2. Find the size of the angle marked x. x 5 cm 5 cm o PLEASE TURN OVER Page 7

8 9. A decimal which goes on forever (infinite) and has a pattern which repeats is called recurring. Dots are often used to show the digits which recur. For example = = The following method can be used to change recurring decimals into fractions. (a) Use this method to change = 0 7 into a fraction. x = x = Subtracting 9x = 4 x = 4 9 In order to change decimals with two recurring digits into a fraction you use the following method. (b) Use this method to change = into a fraction in its lowest form. x = x = Subtracting 99x = 54 x = x = 6 (c) Now use a similar method to change = into a fraction. END OF TEST NOW CHECK YOUR ANSWERS Page 8